MATHEMATICS OF FLIGHT: CROSSWINDS

Transcription

1 MTHEMTIS OF FLIGHT: ROSSWINDS Students will have a basic understanding of math applications used in flight. This includes the effects of crosswinds on aircraft course and direction. Students will solve a series of problems. (One in a series) LESSON PLN Lesson Objectives The students will: e introduced to formulas used in flight related to navigation and aircraft performance. Learn to calculate the effects of crosswinds on aircraft course and direction. Goal In this lesson, students will gain an understanding of common calculations performed by flight personnel. Grade Level: High School-Trigonometry ommon ore State Standards for Mathematics: Trigonometric Functions: Model periodic phenomena with trigonometric functions, prove and apply trigonometric identities Technology ontent Standards (from STL): Technology and Society rosswinds Wind often causes an aircraft to drift from its heading or direction. Pilots must calculate the effect the wind will have on the aircraft so they can remain on course. D In still air, an aircraft would travel due east along. With a crosswind blowing un the direction of, the aircraft actually travels in the direction of D. D represents the course of the aircraft. D is called the drift angle. Materials Required: Paper Pencil or pen Trigonometric Tables alculator (optional) Example: Find the course, the speed of the wind and the drift angle of an aircraft headed at 120 when flying at 240 knots in still air if there is a crosswind of 20 knots blowing from the direction 40. Solution: Draw a diagram to illustrate the problem.

2 X N 40 D 120 ltered ourse Wind 20 knots Original Heading 240 knots Drift ngle X is the drift angle. XD + X = 180 (120-40) + X = X = X - 80 = X = 100 Using alternate interior angles: X = XD XD = 180 X XD = XD = 80 X = 80 Using ΔX and the Law of osines: c 2 = a 2 X 2 = 2 + X 2 2 (X cos ) X 2 = (2 x 20) (240 cos 80 ) X 2 = ,600 9,600 (0.1736) X 2 = , X 2 = 56,333 X = b 2 2ab cosɵ Using the Law of Sines: sin X = sin X X sin X = sin = sin X = 20 (.09848) = X =

3 Exercise 1: pilot is to fly on course 72 in a wind blowing 30 knots from a direction of 134. If the aircraft s speed is 280 knots, in what direction must the pilot head the aircraft and what will be the speed of the aircraft in the wind? N X X = X = 180 ( ) = 118 sin X = sin X sin X = sin = sin X = 30 (0.8829) = X = 5.43 The aircraft heading must be = 77.4 To find the speed in the wind, X = X - X X = X = 56.57

4 X = 280 sin X sin X X = 280 sin sin X = 280 (sin ) sin X = 280 (0.8346) X = knots Exercise 2: n aircraft is headed in direction 120 with a speed of 180 knots in still air. The wind is blowing from 178 at 50 knots. What will be the course of the aircraft? What will be the speed of the aircraft in the wind? (Round answer to the nearest hundredth.) N X Using alternate interior angles: X = X = = 58 Using X and the Law of osines: c 2 = a 2 X 2 = 2 + X 2 2 (X cos X) X 2 = (2 x 50) (180 cos 58 ) X 2 = 2, ,400 18,000 (0.5299) X 2 = 2, ,400 9, X 2 = 25, X = The aircraft will travel at knots. + b 2 2ab cosɵ

5 Using the Law of Sines: sin X = sin X X sin X = sin = sin X = 20 (.09848) = X = See student worksheet and presentation. Resources: National Museum of the United States ir Force elcher, Diana. Education in Flight: Teacher s Guide to the Mathematics of Flight. Department of the ir Force, 2007.

6 MTHEMTIS OF FLIGHT: ROSSWINDS STUDENT WORKSHEET NME: Exercise 1: pilot is to fly on course 72 in a wind blowing 30 knots from a direction of 134. If the aircraft s speed is 280 knots, in what direction must the pilot head the aircraft and what will be the speed of the aircraft in the wind? (Round answer to the nearest hundredth.)

7 MTHEMTIS OF FLIGHT: ROSSWINDS ONTINUED STUDENT WORKSHEET Exercise 2: n aircraft is headed in direction 120 with a speed of 180 knots in still air. The wind is blowing from 178 at 50 knots. What will be the course of the aircraft? What will be the speed of the aircraft in the wind? (Round answer to the nearest hundredth.)